Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.
cot α sin α

검증된 단계별 안내

Recall the definition of cotangent: \( \cot \alpha = \frac{\cos \alpha}{\sin \alpha} \).

Substitute the definition of \( \cot \alpha \) into the expression: \( \cot \alpha \sin \alpha = \frac{\cos \alpha}{\sin \alpha} \cdot \sin \alpha \).

Observe that the \( \sin \alpha \) in the numerator and denominator cancel each other out.

Simplify the expression to \( \cos \alpha \).

Conclude that the expression simplifies to a single trigonometric function: \( \cos \alpha \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Cotangent Function

The cotangent function, denoted as cot(α), is the reciprocal of the tangent function. It can be expressed as cot(α) = cos(α) / sin(α). Understanding cotangent is essential for simplifying expressions involving trigonometric functions, particularly when combined with sine or cosine.

Sine Function

The sine function, sin(α), is a fundamental trigonometric function that relates the angle α to the ratio of the length of the opposite side to the hypotenuse in a right triangle. It is crucial for simplifying expressions that involve angles and is often used in conjunction with other trigonometric identities.

Fundamental Trigonometric Identities

Fundamental trigonometric identities are equations that relate the various trigonometric functions to one another. These include identities such as sin²(α) + cos²(α) = 1 and the reciprocal identities. Utilizing these identities is key to simplifying trigonometric expressions effectively.

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.cot α sin α